Spectral Sampling Method for Uncertainty Propagation in Long-Wave Runup Modeling

Journal of Hydraulic Engineering

Volumn 137, Issue 3, 2010, Pages 277-288

  Ge, Liang ^a   Cheung, Kwok Fai ^b  

^a OCEANIT LABORATORIES INC   (United States)

^b UNIVERSITY OF HAWAII   (United States)

Author keywords

Floods; Long waves; Monte Carlo method; Polynomials; Shallow water; Stochastic models

Indexed keywords

A-PLANE; BREAKING WAVES; DISCONTINUOUS PROCESS; ENSEMBLE AVERAGES; FLOW PARAMETERS; GODUNOV-TYPE SCHEMES; HAZARD MAPPING; LONG WAVE EQUATIONS; LONG WAVES; MODEL INPUTS; NUMERICAL EXAMPLE; ORTHOGONAL MODES; POLYNOMIAL CHAOS; SHALLOW WATERS; SPECTRAL PROJECTIONS; SPECTRAL SAMPLING; STATISTICAL DISTRIBUTION; STATISTICAL PROPERTIES; STOCHASTIC APPROACH; UNCERTAINTY PROPAGATION; WAVE MODELS; WAVE RUNUP; WAVE TRANSFORMATIONS;

ENERGY DISSIPATION; FLOODS; NONLINEAR EQUATIONS; POLYNOMIALS; RAIN; SAMPLING; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; WAVE EQUATIONS; WAVES;

MONTE CARLO METHODS;

BREAKING WAVE; ENERGY DISSIPATION; FLOODING; MONTE CARLO ANALYSIS; STOCHASTICITY; UNCERTAINTY ANALYSIS; WAVE EQUATION; WAVE MODELING; WAVE PROPAGATION; WAVE RUNUP;

EID: 79952326093     PISSN: 07339429     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)HY.1943-7900.0000301     Document Type: Article

References (35)

1. Blumberg A.F. Georgas N. Quantifying uncertainty in estuarine and coastal ocean circulation modeling. J. Hydraul. Eng. 2008, 134(4):403-415. JHEND8, 0733-9429, 10.1061/(ASCE)0733-9429(2008)134:4(403), and.
2. Bradford S.F. Sanders B.F. Finite-volume model for shallow-water flooding of arbitrary topography. J. Hydraul. Eng. 2002, 128(3):289-298. JHEND8, 0733-9429, 10.1061/(ASCE)0733-9429(2002)128:3(289), and.
3. Briggs M.J. Synolakis C.E. Harkins G.S. Green D. Laboratory experiments of tsunami runup on a circular island. Pure Appl. Geophys. 1995, 144(3):569-593. PAGYAV, 0033-4553, 10.1007/BF00874384, and.
4. Brocchini M. Dodd N. Nonlinear shallow water equations modeling for coastal engineering. J. Waterway, Port, Coastal, Ocean Eng. 2008, 134(2):104-120. JWPED5, 0733-950X, 10.1061/(ASCE)0733-950X(2008)134:2(104), and.
5. Carrier G.F. Wu T.T. Yeh H. Tsunami runup and drawdown on a plane beach. J. Fluid Mech. 2003, 475:79-99. JFLSA7, 0022-1120, 10.1017/S0022112002002653, and.
6. Crestaux T. Le Maître O.P. Martinez J.M. Polynomial chaos expansion for sensitivity analysis. Reliab. Eng. Syst. Saf. 2009, 94(7):1161-1172. RESSEP, and.
7. Debusschere B.J. Najm H.N. Pebay P.P. Knio O.M. Ghanem R.G. Le Maître O.P. Numerical challenges in the use of polynomial chaos representations for stochastic processes. SIAM J. Sci. Comput. 2004, 26(2):698-719. SJOCE3, 1064-8275, 10.1137/S1064827503427741, and.
8. Fraccarollo L. Toro E.F. Experimental and numerical assessment of the shallow water model for two-dimensional dam break type problems. J. Hydraul. Res. 1995, 33(6):843-864. JHYRAF, 0022-1686, 10.1080/00221689509498555, and.
9. Gautschi W. Orthpol-a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Softw. 1994, 20(1):21-62. ACMSCU, 0098-3500, 10.1145/174603.174605.
10. Ge L. Cheung K.F. Kobayashi M.H. Stochastic solution for uncertainty propagation in nonlinear shallow-water equations. J. Hydraul. Eng. 2008, 134(12):1732-1743. JHEND8, 0733-9429, 10.1061/(ASCE)0733-9429(2008)134:12(1732), and.
11. Geist E.L. Parsons T. Probabilistic analysis of tsunami hazards. Nat. Hazards 2006, 37(3):277-314. NAHZEL, 0921-030X, 10.1007/s11069-005-4646-z, and.
12. Ghanem R.G. Ingredients for a general purpose stochastic finite element formulation. Comput. Methods Appl. Mech. Eng. 1999, 168(1):19-34. CMMECC, 0045-7825, 10.1016/S0045-7825(98)00106-6.
13. Ghanem R.G. Hayek B. Probabilistic modeling of flow over rough terrain. J. Fluids Eng. 2002, 124(1):42-50. JFEGA4, 0098-2202, 10.1115/1.1445138, and.
14. Ghanem R.G. Spanos P. Stochastic finite elements: A spectral approach 1991, 214. and Springer-Verlag, New York.
15. Gottlieb D. Xiu D.B. Galerkin method for wave equations with uncertain coefficients. Commun. Comput. Phys. 2008, 3(2):505-518. 1815-2406, and.
16. Horritt M.S. Stochastic modelling of 1-D shallow water flows over uncertain topography. J. Comput. Phys. 2002, 180(1):327-338. JCTPAH, 0021-9991, 10.1006/jcph.2002.7097.
17. Hubbard M.E. Dodd N. A 2D numerical model of wave runup and overtopping. Coastal Eng. 2002, 47(1):1-26. COENDE, 0378-3839, 10.1016/S0378-3839(02)00094-7, and.
18. James M. Powell D. Approximation theory and methods 1981, 339. and Cambridge University Press, New York.
19. Lucor D. Meyers J. Sagaut P. Sensitivity analysis of large-eddy simulation to subgrid-scale-model parametric uncertainty using polynomial chaos. J. Fluid Mech. 2007, 585:255-279. JFLSA7, 0022-1120, 10.1017/S0022112007006751, and.
20. Madsen H.O. Krenk S. Lind N.C. Methods of structural safety 1986, 403. and Prentice-Hall, Englewood Cliffs, NJ.
21. Manan A. Cooper J. Design of composite wings including uncertainties: A probabilistic approach. Journal of Aircraft 2009, 46(2):601-607. JAIRAM, 0021-8669, 10.2514/1.39138, and.
22. Melchers R.E. Structural reliability analysis and prediction 1999, 437. 2nd Ed., John Wiley & Sons, Chichester, England.
23. Melching C.S. Yoon C.G. Key sources of uncertainty in QUAL2E model of Passaic River. J. Water Resour. Plann. Manage. 1996, 122(2):105-113. JWRMD5, 0733-9496, 10.1061/(ASCE)0733-9496(1996)122:2(105), and.
24. Morin G. Cardona J.M. Prince O. Pendola M. Perrin F. Reliability assessment of innovative designs in automotive industry. Struct. Infrastruct. Eng. 2009, 5(5):367-379. 1744-8980, 10.1080/15732470701388736, and.
25. Pan C. Lin B. Mao X.Z. Case study: Numerical modeling of the tidal bore on the Qiantang River, China. J. Hydraul. Eng. 2007, 133(2):130-138. JHEND8, 0733-9429, 10.1061/(ASCE)0733-9429(2007)133:2(130), and.
26. Scheffner N.W. Borgman L.E. Mark D.J. Empirical simulation technique based storm surge frequency analyses. J. Waterway, Port, Coastal, Ocean Eng. 1996, 122(2):93-101. JWPED5, 0733-950X, 10.1061/(ASCE)0733-950X(1996)122:2(93), and.
27. Schueller G.I. Pradlwarter H.J. Uncertainty analysis of complex structural system. Int. J. Numer. Methods Eng. 2009, 80(6-7):881-913. IJNMBH, 0029-5981, 10.1002/nme.2549, and.
28. Soize C. Ghanem R. Physical systems with random uncertainties: Chaos representations with arbitrary probability measure. SIAM J. Sci. Comput. 2004, 26(2):395-410. SJOCE3, 1064-8275, 10.1137/S1064827503424505, and.
29. Sudret B. Global sensitivity analysis using polynomial chaos expansions. Reliability Eng. Syst. Safety 2008, 93(7):964-979. RESSEP, 0951-8320, 10.1016/j.ress.2007.04.002.
30. Synolakis C.E. The runup of solitary waves. J. Fluid Mech. 1987, 185:523-545. JFLSA7, 0022-1120, 10.1017/S002211208700329X.
31. Wei Y. Cheung K.F. Curtis G.D. McCreery C.S. Inverse algorithm for tsunami forecasts. J. Waterway, Port, Coastal, Ocean Eng. 2003, 129(2):60-69. JWPED5, 0733-950X, 10.1061/(ASCE)0733-950X(2003)129:2(60), and.
32. Wei Y. Mao X.Z. Cheung K.F. Well-balanced finite-volume model for long-wave runup. J. Waterway, Port, Coastal, Ocean Eng. 2006, 132(2):114-124. JWPED5, 0733-950X, 10.1061/(ASCE)0733-950X(2006)132:2(114), and.
33. Wiener S. The homogeneous chaos. Am. J. Math. 1938, 60(4):897-936. AJMAAN, 0002-9327, 10.2307/2371268.
34. Xiu D. Karniadakis G.E. Modeling uncertainty in flow simulations via generalized polynomial chaos. J. Comput. Phys. 2003, 187(1):137-167. JCTPAH, 0021-9991, 10.1016/S0021-9991(03)00092-5, and.
35. Zhou J.G. Causon D.M. Mingham C.G. Ingram D.M. The surface gradient method for the treatment of source terms in the shallow-water equations. J. Comput. Phys. 2001, 168(1):1-25. JCTPAH, 0021-9991, 10.1006/jcph.2000.6670, and.